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Matteo Zatti

Publications and source records attributed to Matteo Zatti.

At least 19 recordsLinked to original sources
arXiv2026

Worldsheet functional RG and the $α'$-tower

We apply the functional renormalization group to the worldsheet theory of the bosonic string. Imposing the Weyl anomaly cancellation as a condition on the local renormalization group flow, we derive flow equations for the background couplings and the corresponding effective spacetime equations of motion, first in a two-derivative truncation, on a general curved background. We then consider a truncation to all orders in $α'$, which captures only a subset of the possible tensor structures but is analytically tractable, in analogy with $f(R)$-like approximations. Within this truncation, we obtain Tseytlin's spacetime effective action, and we use it to study solutions to all orders in $α'$, including black holes. Our results show that the functional renormalization group can be implemented on the string worldsheet and provide a framework to access the strong-curvature regime. As a longer-term goal, this may allow one to test the scenario of effective asymptotic safety in string theory, in which an approximately scale-invariant regime lies between the low-energy effective field theory and a stringy completion.

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arXiv2026

How to (Non-)Perturb a BPS Black Hole

We relate the structure of non-perturbative corrections to BPS black hole observables in flat-spacetime theories with certain properties of probe charged particles in the near-horizon geometry. Concretely, we consider 4d $\mathcal{N} = 2$ supergravity with an infinite tower of F-terms and probe branes in $\text{AdS}_2\times \mathbf{S}^2$ backgrounds threaded by constant electric-magnetic fields. The higher dimensional operators we pick are computed by Type II topological string theory, and we approximate them via the constant map contribution, which is valid at large volume and can be interpreted as arising from D0-branes integrated out in M-theory on a Calabi-Yau threefold times a circle. We analyze the resulting force conditions on massive particles carrying $(q_A, p^A)$ charges, their classical trajectories, and the 1-loop effective action they produce. A simple semiclassical analysis allows us to understand qualitatively the structure of the non-perturbative corrections. The exact path integral assessment then reproduces the Gopakumar--Vafa integral of the flat-spacetime theory, now evaluated in the black hole attractor geometry. Thus, we make explicit how the physics of the fully backreacted black hole solution is controlled by the behaviour of the light D-brane states which generate the relevant set of higher derivative corrections.

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arXiv2026

Quantum Calabi-Yau Black Holes and Non-Perturbative D0-brane Effects

We compute the supersymmetric entropy of the most general BPS black hole in 4d $\mathcal{N}=2$ supergravity coupled to $n_V$ vector multiplets obtained from Type IIA string theory compactified on a Calabi-Yau threefold at large volume, including the all-genera leading-order $α'$-corrections. These can be equivalently seen as D0-brane quantum effects from a dual five-dimensional M-theory perspective. We find that these corrections generically lead to both perturbative and non-perturbative contributions to the black hole entropy. We argue that the exception occurs for certain specific configurations where the gauge background, seen through the lens of D0-brane probes, behaves as purely electric or purely magnetic, thereby accounting for the absence of such non-perturbative effects. To explore this further, we perform a semiclassical analysis of the (non-)BPS particle dynamics in the near-horizon geometry of the underlying black hole, which is described by a maximally supersymmetric AdS$_2\times \mathbf{S}^2$ solution. As a byproduct, this study provides additional insights into the (non-perturbative) stability of supersymmetric black hole solutions and suggests an interpretation in terms of complex saddles contributing to the worldline path integral.

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arXiv2026

On Supersymmetric D-brane probes in 4d $\mathcal{N}=2$ $\text{AdS}_2\times\mathbf{S}^2$ Attractors

We extend the $κ$-symmetry analysis of supersymmetric D-brane probes in the $\mathrm{AdS}_2 \times \mathbf{S}^2$ attractor geometry, originally performed by Simons, Strominger, Thompson, and Yin, to also include stationary -- but non-static -- worldlines carrying angular momentum along the 2-sphere. We demonstrate that certain special trajectories, with fixed radius and orbital velocity, solve the equations of motion and moreover satisfy a supersymmetry preserving condition, thus defining new $\frac12$-BPS configurations. Furthermore, these classical paths are shown to saturate a lower bound for the Hamiltonian generating global time translations, with the corresponding minimal energy depending on a generalized angular momentum vector $\boldsymbol{J}$. The direction of the latter, in turn, determines exactly which supercharges remain unbroken. Our results reveal a richer spectrum of (multi-particle) supersymmetric states in $\mathrm{AdS}_2 \times \mathbf{S}^2$, which can be organized into distinct selection sectors labeled by the conserved $SU(2)$ charges. This construction has direct applications in black hole microstate counting, the analysis of probe dynamics and $\text{AdS}_2/\text{CFT}_1$ holography.

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arXiv2026

Exact Path Integral Methods in Supersymmetric $\text{AdS}_2\times \mathbf{S}^2$ Backgrounds

We determine the exact functional determinants of charged, massive spin-0 and spin-$\frac12$ particles in $\text{AdS}_2\times \mathbf{S}^2$ backgrounds threaded by constant electric and magnetic fields. This is achieved using Schwinger proper-time formalism, which allows us to derive the full non-perturbative effective action in the 1-loop and constant background field approximations. We then specialize the computation to supersymmetric settings and we obtain the effective action for a 4d $\mathcal{N}=2$ BPS massive hypermultiplet in a supersymmetric $\text{AdS}_2\times \mathbf{S}^2$ spacetime. This setup can be seen to be equivalent to the near-horizon geometry of a BPS black hole which solves the attractor equations of 4d $\mathcal{N}=2$ supergravity. Our results provide a necessary intermediate step for the evaluation of the quantum-corrected black hole partition function. We also comment on the relation with the celebrated Gopakumar-Vafa integral representation.

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arXiv2025

Black Hole Entropy, Quantum Corrections and EFT Transitions

We revisit and study quantum corrections to the supersymmetric entropy of BPS black holes in 4d $\mathcal{N}=2$ effective field theories (EFTs), which can be obtained from Type IIA string theory compactified on a Calabi-Yau threefold. Macroscopically, these corrections arise from an infinite series of higher-derivative F-terms that encode certain modifications to the two-derivative supergravity effective action. Within the large volume regime, we analyze in detail the moduli dependence of these semi-classical contributions and explore their implications for the black hole entropy. As a byproduct, we show that the entropy captures, in a rather intricate way, the transition between four- and five-dimensional dual EFT descriptions. In fact, the expansion parameter $α$ controlling the relevant asymptotic series can be related to the ratio of the black hole horizon and the Kaluza-Klein scale, given here by the inverse D0-brane mass. Furthermore, we are able to resum the series into a well-behaved convergent expression for all values of $α$. This demonstrates, in turn, that (stable) black holes can, indeed, probe scales besides the quantum gravity cutoff. More precisely, by examining two representative BPS systems -- the D0-D2-D4 and D2-D6 black hole solutions -- we explicitly illustrate how highly non-local (perturbative) quantum effects resolve the divergences, ultimately leading to a well-defined entropy function. Additionally, in certain cases, we show that one can take a suitable decompactification limit to 5d and verify that the corrected entropy function reproduces the exact microstate counting of the underlying five-dimensional black string. Our results also clarify the role of non-perturbative quantum corrections, which, remarkably, do not modify any of our prior conclusions.

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arXiv2025

Exploring String Theory Solutions: Black hole thermodynamics with $α'$ corrections and type II compactifications

This PhD thesis explores the properties of certain solutions in stringy effective field theories (EFTs). In the context of heterotic string theory (HST), we study $α'$ corrections to well-known black hole solutions. We present explicit, analytical expressions for the $α'$ corrections to these solutions and fully characterize their thermodynamics refining Iyer-Wald's prescription. In the context of type II theories, we study compactifications of the form $X_4 \times X_6$. We begin with AdS$_4$ Calabi-Yau orientifold compactifications with localized sources and investigate their non-perturbative stability. We then consider internal manifolds with non-trivial integer (co)homology and demonstrate how integer homology data can leak into the EFT.

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arXiv2024

On the thermodynamics of the black holes of the Cano-Ruipérez 4-dimensional string effective action

The Cano-Ruipérez 4-dimensional string effective action is the simplest consistent truncation of the first-order in $α'$ heterotic string effective action compactified on T$^{6}$. This theory contains, on top of the metric, a dilaton and an axion that couple to the Gauss-Bonnet term and to the Pontrjagin density which suggests a very strong relation between the physical and geometrical properties of its solutions. In this paper we study the thermodynamics of the string black-hole solutions of this theory using Wald's formalism. We construct the on-shell closed generalized Komar, dilaton and axion 2-form charges, and we used them to find the Smarr formula (that we test on the Schwarzschild and Kerr solutions) and to prove no-(primary)-hair theorems for the scalar. We find that $α'$ plays the role of a thermodynamical variable with an associated chemical potential. We also notice the occurrence of non-standard gravitational charges in the Wald entropy and scalar charges.

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arXiv2024

Democratic actions with scalar fields: symmetric sigma models, supergravity actions and the effective theory of the type IIB superstring

The dualization of the scalar fields of a theory into (d-2)-form potentials preserving all the global symmetries is one of the main problems in the construction of democratic pseudoactions containing simultaneously all the original fields and their duals. We study this problem starting with the simplest cases and we show how it can be solved for scalars parametrizing Riemannian symmetric sigma-models as in maximal and half-maximal supergravities. Then, we use this result to write democratic pseudoactions for theories in which the scalars are non-minimally coupled to (p+1)-form potentials in any dimension. These results include a proposal of democratic pseudoaction for the generic bosonic sector of 4-dimensional maximal and half-maximal ungauged supergravities. Furthermore, we propose a democratic pseudoaction for the bosonic sector of N=2B,d=10 supergravity (the effective action of the type IIB superstring theory) containing two 0-, two 2-, one 4-, two 6- and three 8-forms which is manifestly invariant under global SL(2,R) transformations.

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arXiv2024

Gravitational higher-form symmetries and the origin of hidden symmetries in Kaluza-Klein compactifications

We show that, in presence of isometries and non-trivial topology, the Einstein--Hilbert action is invariant under certain transformations of the metric which are not diffeomorphisms. These transformations are similar to the higher-form symmetries of field theories with $p$-form fields. In the context of toroidal Kaluza--Klein compactifications, we show that these symmetries give rise to some of the ``hidden symmetries'' (dualities) of the dimensionally-reduced theories.

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arXiv2024

Revisiting $α'$ corrections to heterotic two-charge black holes

We find solutions of the heterotic string effective action describing the first-order $α'$ corrections to two-charge black holes at finite temperature. Making explicit use of these solutions, we compute the corrections to the thermodynamic quantities: temperature, chemical potentials, mass, charges and entropy. We check that the first law of black hole mechanics is satisfied and that the thermodynamics agrees with the one extracted from the Euclidean on-shell action. Finally, we show that our results are in agreement with the corrections for the thermodynamics recently predicted by Chen, Maldacena and Witten.

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arXiv2023

Extremal stringy black holes in equilibrium at first order in $α'$

We compute the first-order $α'$ corrections to well-known families of heterotic multi-center black-hole solutions in five and four dimensions. The solutions can be either supersymmetric or non-supersymmetric, depending on the relative sign between two of the black-hole charges. For both cases, we find that the equilibrium of forces persists after including the $α'$ corrections, as the existence of multi-center solutions free of unphysical singularities shows. We analyze the possibility of black-hole fragmentation.

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arXiv2023

$α'$ corrections to 4-dimensional non-extremal stringy black holes

We compute the first-order $α'$ corrections to a family of 4-dimensional, 4-charge, non-extremal black hole solutions of Heterotic Supergravity in the case with 3 independent charges. The solutions are fully analytic, reproduce the extremal limit previously found in the literature and, applying T-duality, they transform as expected. If we reduce to the case with a single independent charge we obtain the corrections to four embeddings of the Reissner-Nordström black hole in string theory. We completely characterize the black hole thermodynamics computing the Hawking temperature, Wald entropy, mass, gauge charges and their dual thermodynamic potentials. We verify that all these quantities are related by the first law of extended black hole mechanics and the Smarr formula once we include a potential associated to the dimensionful parameter $α'$ and the scalar charges. We found that the latter are not identified with the poles at infinity of the scalar fields because they receive $α'$ corrections.

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arXiv2023

Torsion in cohomology and dimensional reduction

Conventional wisdom dictates that $\mathbb{Z}_N$ factors in the integral cohomology group $H^p(X_n, \mathbb{Z})$ of a compact manifold $X_n$ cannot be computed via smooth $p$-forms. We revisit this lore in light of the dimensional reduction of string theory on $X_n$, endowed with a $G$-structure metric that leads to a supersymmetric EFT. If massive $p$-form eigenmodes of the Laplacian enter the EFT, then torsion cycles coupling to them will have a non-trivial smeared delta form, that is an EFT long-wavelength description of $p$-form currents of the $(n-p)$-cycles of $X_n$. We conjecture that, whenever torsion cycles are calibrated, their linking number can be computed via their smeared delta forms. From the EFT viewpoint, a torsion factor in cohomology corresponds to a $\mathbb{Z}_N$ gauge symmetry realised by a Stückelberg-like action, and calibrated torsion cycles to BPS objects that source the massive fields involved in it.

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arXiv2023

On scalar charges and black-hole thermodynamics

We revisit the first law of black hole thermodynamics in 4-dimensional theories containing scalar and Abelian vector fields coupled to gravity using Wald's formalism and a new definition of scalar charge as an integral over a 2-surface which satisfies a Gauss law in stationary black-hole spacetimes. We focus on ungauged supergravity-inspired theories with symmetric sigma models whose symmetries generate electric-magnetic dualities leaving invariant their equations of motion. Our manifestly duality-invariant form of the first law is compatible with the one obtained by of Gibbons, Kallosh and Kol. We also obtain the general expression for the scalar charges of a stationary black hole in terms of the other physical parameters of the solution and the position of the horizon, generalizing the expression obtained by Pacilio for dilaton black oles.

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arXiv2023

Wald entropy in Kaluza-Klein black holes

We study the thermodynamics of the 4-dimensional electrically charged black-hole solutions of the simplest 5-dimensional Kaluza-Klein theory using Wald's formalism. We show how the electric work term present in the 4-dimensional first law of black-hole thermodynamics arises in the purely gravitational 5-dimensional framework. In particular, we find an interesting geometric interpretation of the 4-dimensional electrostatic potential similar to the angular velocity in rotating black holes. Furthermore, we show how the momentum map equation arises from demanding compatibility between the timelike Killing vector of the black-hole solution and the spatial Killing vector of the 5-dimensional background.

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arXiv2022

Non-extremal, $α'$-corrected black holes in 5-dimensional Heterotic Superstring Theory

We compute the first-order $α'$ corrections of the non-extremal Strominger-Vafa black hole and its non-supersymmetric counterparts in the framework of the Bergshoeff-de Roo formulation of the heterotic superstring effective action. The solution passes several tests: its extremal limit is the one found in an earlier publication and the effect of a T duality transformation on it is another solution of the same form with T dual charges. We compute the Hawking temperature and Wald entropy showing that they are related by the first law and Smarr formula. On the other hand, these two contain additional terms in which the dimensionful parameter $α'$ plays the role of thermodynamical variable.

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